Truncated Multiplication computes a truncated product, a contiguous subsequence of the digits of the product of 2 long integers. We review a few truncated multiplication algorithms and adapt them to integers. They are a constant times faster than n-digit full multiplications of time complexity O(n), with 1< α ≤ 2, important in cryptography. For example, the least significant half products with ...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...